Question

A primary school enrolls 250 girls and a number of boys. At this

school, the ratio of girls to boys enrolled is p: q. At a school event of
180 students from the school, 30 of them are girls and the ratio of the
number of girls attending this event to the number of boys attending, is
the same p : q. How many students are enrolled at the primary school
(A) 1250
(B) 1500
(C) 1750
(D) 1800
(E) 2000

Answer 1

From the information above, we can create the following equation to represent the ratio of girls to boys at the school event: 30/(180-30) p/q Simplifying this equation, we get: 30/150= p/q 4. Now, we can set up a proportion using the information from the previous step: 30/150 p/q 5. We can solve this proportion to find the value of q: Cross-multiply: 30 g 150 p Divide both sides bv 30: q (150 p)/30 Simplify: q=5p 6. Since the ratio of girls to boys enrolled in the primary school is p: a. and the ratio of girls to boys attending the school event is p: q, we can conclude that the ratio of girls Ask another question

Answer 2

By establishing that the ratio of girls to boys is the same in both the school and the event, we calculate the total number of boys as 1250. Thus, the total enrollment at the primary school is 1500 students.

Step-by-step explanation:

The student's question involves solving a problem related to ratios and proportions in a primary school setting. The school enrolls 250 girls and boys in an unknown number, maintaining a ratio of p:q between girls and boys. During a school event, 30 girls attend, and the total number of students is 180, with the same p:q ratio.

We know there were 180 students at the event and 30 of them were girls. The event had the same girl-to-boy ratio as the whole school population, so we can set up a proportion:

If the ratio is p:q and there are 30 girls, then the number of boys is (q/p) * 30. Because the total number of students at the event equals the number of girls plus the number of boys, we get:

30 + (q/p) * 30 = 180 students. Simplifying this, we find that q/p is 5.

Back to the entire school, we know there are 250 girls. If the ratio of girls to boys is p:q and q/p is 5, then the number of boys is 5 * 250 = 1250. Hence, the total number of students is 250 girls + 1250 boys, which amounts to 1500 students.

Therefore, the correct answer is (B) 1500.